Higher order refined computational models for the stability analysis of FGM plates – Analytical solutions

• This theory considers both transverse shear and normal deformation.
• Realistic variation of displacements and strains considered.
• Quantitative assessment of models done for the first time.
• Very accurate compared to other models considered in the present study.
• The presented results will set a benchmark for future investigations.

Analytical formulations and solutions for the stability analysis of simply supported Functionally Graded Material (FGM) sandwich plates hitherto not reported in the literature based on two higher-order refined computational models available in the literature are presented. These computational models are based on Taylor's series expansion of the displacements in the thickness coordinate and incorporate the realistic parabolic distribution of transverse strains through the plate thickness. One of them with twelve degrees-of-freedom considers the effects of both transverse shear and normal strain/stress while the other with nine degrees-of-freedom includes only the effect of transverse shear deformation. In addition another higher-order model and the first-order model developed by other investigators and available in the literature are also considered for the evaluation purpose. For mathematical modeling purposes, the Poisson's ratio of the material is considered as constant whereas Young's modulus is assumed to vary through the thickness according to the power law function. The governing equations of equilibrium for buckling analysis are obtained using the Principle of Minimum Potential Energy (PMPE). Solutions are obtained in closed form using Navier's technique by solving the eigenvalue problem. The comparison of the present results with the available elasticity solutions and the results computed independently using the first-order and another higher-order theory available in the literature shows that the higher-order refined theory with 12 degrees-of-freedom predicts the critical buckling load more accurately than all other theories considered in this paper. After establishing the accuracy of prediction, extensive numerical results for FGM sandwich plates using all the models are presented which will serve as a benchmark for future investigations.